Background: Applications of Eyring-Powell fluid is found in paint industries, pharmaceutical companies and armour construction. Eyring-Powell fluid models are able to model Newtonian and shear-thinning fluids under different conditions, but researchers have reported seemingly contradicting results based on the effects of Eyring-Powell parameter on flow velocity. Methods: This paper shows that Eyring Powell fluid can also exhibit shear-thickening properties when certain conditions are imposed. By introducing this condition on Eyring-Powell model, a new class of Modified Eyring-Powell fluid is presented in this study, which clearly shows why different results are obtained by different researchers. A theoretical analysis of the heat transfer is carried out on the flow of MEP on a linearly stretching flat plate and the results are depicted as graphs and tables. Significant Findings: It is found that increasing Prandtl number causes a decrease in the temperature. Under shear-thinning condition, increasing the Eyring-Powell parameters leads to a decrease in both skin-friction coefficient and heat transfer rate. Under shear-thickening condition, increasing the Eyring-Powell parameters leads to an increase in both skin-friction coefficient and heat transfer rate.